yichijin

I wanted to add one detail--there actually are ways to do early stopping while staying within a frequentist approach. For example, most clinical trials methods are not Bayesian but rather are just fixed-horizon tests that have the allowable amount of Type 1 error "spread out" amongst the multiple looks that are planned in advance.

At Optimizely we essentially have a continuous version of this that does in fact allow for multiple looks with rigorous control of Type 1 error. As tedsanders mentions, the key upside is that if you start an experiment with a larger-than-expected lift, you can terminate it early. Then over many repeated experiments, you gain a lot in terms of average time to significance.

The dissonance in this discussion mostly stems from the fact that this paper (which we actually collaborated on!) uses data from 2014, before we rolled out this new Stats Engine.

Take a look at clinical trials. Often in clinical trials there are multiple phases, where early stopping is desirable in case the drug has higher-than-expected efficacy (or more-harmful-than-expected side effects).

The type of test conducted in clinical trials explicitly allow for multiple looks while maintaining correct control of the Type 1 error rate. At Optimizely we essentially have a version of this where the monitoring can be conducted contiuously with rigorous control of Type 1 error.

We were excited to collaborate with the authors on this study. Keep in mind the data used in this analysis is from 2014, before we introduced sequential testing and FDR correction as to specifically address this p-hacking issue. I expect these results are in line with any platform using fixed-horizon frequentist methods.